The related literature on Naive-Bayes classification can generally be sorted into four categories - structure extension, feature selection, attribute weighting and local learning. As described previously, one drawback of the Naive-Bayes algorithm is the attribute independence assumption. Structure extension tackles this problem by determining feature or attribute dependencies. Often, approaches utilize the factor graph representation of probability distributions to depict the Bayesian network. Learning the optimal Bayesian network is regarded as an intractable problem and researchers usually employ techniques to reduce the complexity. One such method is described in [1]} where the author uses a directed graph to represent the distribution. They refer to this method as Tree Augmented Naive Bayes or TAN. The structure of the TAN graph is limited in that features can have at most two parents, one parent must be the class and the other parent can be an attribute. These constraints reduce the complexity of learning and the problem formulates as \(p(C=c|\mathbf {X}=[X_1,X_2, \ldots , X_n])\)  with learning occurring in polynomial time. TAN allows for edges between child vertices (attributes), and hence creates dependencies between attributes, reducing the independence assumption of the Naive-Bayes classifier.
